2000 Fiscal Year Annual Research Report

強擬凸CR構造と接触構造の幾何と解析

Research Project

Project/Area Number	11440019
Research Institution	Nagoya University
Principal Investigator	内藤久資名古屋大学, 大学院・多元数理科学研究科, 助教授 (40211411)
Co-Investigator(Kenkyū-buntansha)	金井雅彦名古屋大学, 大学院・多元数理科学研究科, 教授 (70183035) 江尻典雄名古屋大学, 大学院・多元数理科学研究科, 助教授 (80145656) 佐藤肇名古屋大学, 大学院・多元数理科学研究科, 教授 (30011612) 中西敏浩名古屋大学, 大学院・多元数理科学研究科, 助教授 (00172354) 小林亮一名古屋大学, 大学院・多元数理科学研究科, 教授 (20162034)
Keywords	ヤン・ミルズ勾配流 / ケーラー計量 / サイバーグ・ウィテン方程式 / 負曲率多様体 / 接触構造 / クライン群 / CR幾何 / ビルディング
Research Abstract	研究代表者・内藤久資は,ヤン・ミルズ汎関数の勾配流として与えられる多様体上の非線型熱方程式について研究を行い,解が有限時間内に爆発する例を与えた. 研究分担者・佐藤肇は,グラスマン構造など種々の構造の間のツイスター対応と,それら構造の積分可能条件について研究を行った. 江尻典雄は,リーマン行列の微分幾何学的特徴付けを考えて,微分幾何的ショットキー問題を研究した. 金井雅彦は,双曲的な閉多様体の基本群の球面への標準的な共形的作用が局所剛性をもつことを証明した. 小林亮一は,リッチ平坦なケーラー計量の存在問題,正則曲線の値分布論における対数微分の補題の精密化について研究し,アーベル多様体の場合に第2主要定理を証明した. 芥川和雄は,境界付き多様体の相対山辺不変量,およびサイバーグ・ウィッテン方程式について研究した. 中西敏浩は,穴あき曲面群のSL(2,C)表現の空間に座標系を与え,写像類群の作用について研究した. 小谷元子は,周期的な非コンパクト多様体の熱核,および結晶格子上のランダムウォークの推移確率の時間無限大での漸近挙動を調べた.また,負曲率閉多様体の閉測地線で,ホモローグなものの個数の漸近挙動を調べた. 納谷信は,鎌田博行と共同で,CR幾何の四元数的類似の研究を行った.また,ビルディングから非正曲率空間への区分的にアファインな写像で,あるエネルギーを最小化するものについて研究を行った. 相山玲子は,4次元Euclid空間への曲面のはめ込みについて研究し,はめ込み写像は(局所的には)2つの角度関数によって定まる1階線形微分方程式系の解として与えられることをみた. 太田啓史は,フレアーコホモロジーに対する障害理論を構築するとともに,ラグランジアン部分多様体に対し,フィルター付きA_∞代数を構成した.また,タイトだがフィラブルでない接触構造の存在を明らかにした. 井関裕靖は,正スカラー曲率をもつコンパクトな共形平坦多様体を与えるクライン群が凸ココンパクトであることを,A種数の指数定理を応用することにより証明した. 鎌田博行は,コンパクト複素曲面上の自己双対な不定値ケーラー計量の存在問題を考察し,複素射影曲線の直積上にそのような計量の族を具体的に構成し,それらが等長的となる条件について研究した. 石毛和弘は,熱方程式の非負値解の構造について研究を行った.特に,非有界領域における様々な条件下において,どのように非負値解の構造が変わるかを研究した.

Research Products

(40 results)

All Other

All Publications (40 results)

[Publications] 内藤久資: "4次元多様体上のYang-Mills heat flowの小さな初期値をもつ解について"数理解析研究所講究録. 1076. 57-64 (1999)
[Publications] 内藤久資: "高次元におけるYang-Mills heat flowの解の爆発について"数理解析研究所講究録. 1117. 36-43 (1999)
[Publications] 佐藤肇: "Schwarzian derivatives of Contact diffcomorphiswas"Lobacheoshii J.Math.. 4. 89-98 (1999)
[Publications] 佐藤肇,小沢哲也: "Liveasization of adinary differential equations by ana preserving maps"Nagoya Math.J.. 156. 109-122 (1999)
[Publications] 佐藤肇: "Intequability of contact Schwaizian derivatives and its liveasization"Geovetry, Integrability and Quatiration. 225-228 (2000)
[Publications] 佐藤肇,待田芳徳: "Tuistor theory of manifolds with. Grassmannian structures"Nagoya Math.J.. 160. 17-102 (2000)
[Publications] 鎌田博行: "Neutral hyperkahler structures on primary kodaira surfaces"Tsukuba J.Math.. 23. 321-332 (1999)
[Publications] 鎌田博行: "Compact Einstein-weyl four-manifolds with compatible about complex structuses"Kodai Math.J.. 22. 424-437 (1999)
[Publications] 石毛和弘: "On the behavior of the Polutions of degenerate parabolic equations"Magoya Math.J,. 155. 1-26 (1999)
[Publications] 石毛和弘: "An intrinsic metric approach to unigue wess of the positive Divichlit prodders for pacalohi quchious in cylinder"J.Differcmfial Equathions. 158. 251-290 (1999)
[Publications] 小谷元子: "グラフの幾向学"数理科学. 39. (2001)
[Publications] 納谷信: "Discrele groups of couplex hyperbolic isometries and psendo-Hunitian strnctures"Trends in Math., Analysis and pometry in several couplex vaiables. 209-237 (1999)
[Publications] 太田啓史,小野薫: "Simple singularities and topology of symplectically filling 4-manifold"Commsut.Math.Helv.. 74. 575-590 (1999)
[Publications] 太田啓史: "Brieskovn manifold and metric of positive scalas curvature"Adiaucid Studies Puse Math. 29(to appear).
[Publications] 太田啓史: "Obstruchas to and deformation of Laqraugias Mtuseehls Floes cohomology"Proc.of Uarls Shop on"Mirrov Supnnietry and Syunplechz gesnetry". (to appear).
[Publications] 井関裕靖: "Quasiconformal stability of Kleiuian qroups and au cnbedding of auyace of flat andcind structuses"Conform.Geour.Dyn. 4. 108-119 (2000)
[Publications] 小谷元子,砂田利一: "Albanese maops and off siagonal long time asepuptotics for the heat hernels"Comm.Math.Phys.. 209. 633-670 (2000)
[Publications] 小谷元子: "A mote on aryouptotic expanoipus for closed geodetics or homologer clesses"Math.Aun.. (to appear).
[Publications] 小谷元子: "A central limit theaem for the simple randow wallc on a crystal lathic"Droe.Second Intermat.ISAAC Corgress. 1-7 (2000)
[Publications] 小谷元子,砂田利一: "Zata fucehions on finite graphs"J.Marh.Sci.Univ.Tokyo. 7. 7-25 (2000)
[Publications] 小谷元子,砂田利一: "The pressune and higher correlations for an Auosov differworplisus"Erqod.Th.Dynam.Sys. (to appear).
[Publications] 小谷元子: "Higher correlations for an Anosiv flow"Aues.J.Math. (to appear).
[Publications] 芥川和雄: "Spin geometry, the Seiberg-Uithen eguiations and Yamabe invasiints of Kahler sufaces"Interdiscip.Inform.Sci.. 5. 55-72 (1999)
[Publications] 中西敏浩,M.Naatanen: "Areas of two-dinaousional moduli apaces"Proc.Aum.Math.Soc,. (to appear).
[Publications] 中西敏浩,M.Naataven G,Rosenberger: "Arithmetic Fuchsian groups of siguatuce (o;ei, er,es,en)with 2【less than or equal】e_1【less than or equal】e_2【less than or equal】e_3, en=∞"Couplex geometry of groups. (1999)
[Publications] 中西敏浩: "リーマン面上の割地線の長さとNielsenの実現問題"退化、被覆、特異点の代数幾向とトポロジー. 33-46 (2000)
[Publications] 小谷元子,砂田利一: "Jacobian fovi associated with a finite graple and its abelian couning graphs"Adu.Appl.Math.. 24. 89-110 (2000)
[Publications] 小谷元子,砂田利一: "Stund and veelizatron of crystal lattice via hainouic maps"Traw.Ames.Math.Soc.. 353. 1-20 (2001)
[Publications] 相山玲子,芥川和雄: "Kenmotsu type representation fornnla for spece like sunfaus in the de Sitha 3-space"Tsukuba J.Math.. 24. 189-196 (2000)
[Publications] 相山玲子,芥川和雄: "Kenmotsu type representation fovmula for surfaces with preseribed mean cuwatuse in the hypablic3-space"J.Math.Soc.Japan. 52. 877-898 (2000)
[Publications] 相山玲子,芥川和雄,Tom Y.M.Wan: "Hininal maps between the hyperbolic discs and genealped Qoues maps of maxineal simfaics in the auti-de siffer3-space"Tohoku Math.J.. 52. 415-429 (2000)
[Publications] 相山玲子,芥川和雄: "kenmotsu type representation forunla for surfaces with prescrived mean curoatue in the 3-sphere"Tohoku Math.J.. 52. 95-105 (2000)
[Publications] 相山玲子,芥川和雄: "Represeu tation formulas for surfaces in H^s(-C^2)and havmonic maps arising from CMC surfaces"Harmonic movphisms, Hamouic maps, and related topics. 275-285 (2000)
[Publications] 相山玲子,芥川和雄,宮岡礼子,梅原雅顕: "A global correspondence between CMC-Surfaces in S^3 and paices of non-conformal hamouic mapsinto S^2"Proc.Amer.Math.Soc.. 128. 939-941 (2000)
[Publications] 江尻典雄: "Homotopieally enesqy-minimizing hasimocne map of fori into RR^3"TokyoJ.Math. 23. 503-518 (2000)
[Publications] 金井雅彦: "力学系の不変幾何構造と剛性問題"数学. 52. 43-52 (2000)
[Publications] 金井雅彦: "A remanls on local rigidity of comfor〓l actions on the sphere"Math.Res.Lett. 6. 675-680 (1999)
[Publications] 小林亮一,逸見昌元: "Hoal's law in ptatistical manifolds and diver gances"Nayoya math.J.. 159. 1-24 (2000)
[Publications] 小林亮一: "Holomovphic curves in abelian vacieties : the second main theouew and appdicatious"Japan.J.Math.. 26. 129-152 (2000)
[Publications] 小林亮一,系川銚: "Msuimizing currents in open manifolds andf the n-1 homology of monue gatively Ricci curved niani folds"

2000 Fiscal Year Annual Research Report

強擬凸CR構造と接触構造の幾何と解析

Principal Investigator

内藤 久資 名古屋大学, 大学院・多元数理科学研究科, 助教授 (40211411)

Research Products

[Publications] 内藤久資: "4次元多様体上のYang-Mills heat flowの小さな初期値をもつ解について"数理解析研究所講究録. 1076. 57-64 (1999)

[Publications] 内藤久資: "高次元におけるYang-Mills heat flowの解の爆発について"数理解析研究所講究録. 1117. 36-43 (1999)

[Publications] 佐藤肇: "Schwarzian derivatives of Contact diffcomorphiswas"Lobacheoshii J.Math.. 4. 89-98 (1999)

[Publications] 佐藤肇,小沢哲也: "Liveasization of adinary differential equations by ana preserving maps"Nagoya Math.J.. 156. 109-122 (1999)

[Publications] 佐藤肇: "Intequability of contact Schwaizian derivatives and its liveasization"Geovetry, Integrability and Quatiration. 225-228 (2000)

[Publications] 佐藤肇,待田芳徳: "Tuistor theory of manifolds with. Grassmannian structures"Nagoya Math.J.. 160. 17-102 (2000)

[Publications] 鎌田博行: "Neutral hyperkahler structures on primary kodaira surfaces"Tsukuba J.Math.. 23. 321-332 (1999)

[Publications] 鎌田博行: "Compact Einstein-weyl four-manifolds with compatible about complex structuses"Kodai Math.J.. 22. 424-437 (1999)

[Publications] 石毛和弘: "On the behavior of the Polutions of degenerate parabolic equations"Magoya Math.J,. 155. 1-26 (1999)

[Publications] 石毛和弘: "An intrinsic metric approach to unigue wess of the positive Divichlit prodders for pacalohi quchious in cylinder"J.Differcmfial Equathions. 158. 251-290 (1999)

[Publications] 小谷元子: "グラフの幾向学"数理科学. 39. (2001)

[Publications] 納谷信: "Discrele groups of couplex hyperbolic isometries and psendo-Hunitian strnctures"Trends in Math., Analysis and pometry in several couplex vaiables. 209-237 (1999)

[Publications] 太田啓史,小野薫: "Simple singularities and topology of symplectically filling 4-manifold"Commsut.Math.Helv.. 74. 575-590 (1999)

[Publications] 太田啓史: "Brieskovn manifold and metric of positive scalas curvature"Adiaucid Studies Puse Math. 29(to appear).

[Publications] 太田啓史: "Obstruchas to and deformation of Laqraugias Mtuseehls Floes cohomology"Proc.of Uarls Shop on"Mirrov Supnnietry and Syunplechz gesnetry". (to appear).

[Publications] 井関裕靖: "Quasiconformal stability of Kleiuian qroups and au cnbedding of auyace of flat andcind structuses"Conform.Geour.Dyn. 4. 108-119 (2000)

[Publications] 小谷元子,砂田利一: "Albanese maops and off siagonal long time asepuptotics for the heat hernels"Comm.Math.Phys.. 209. 633-670 (2000)

[Publications] 小谷元子: "A mote on aryouptotic expanoipus for closed geodetics or homologer clesses"Math.Aun.. (to appear).

[Publications] 小谷元子: "A central limit theaem for the simple randow wallc on a crystal lathic"Droe.Second Intermat.ISAAC Corgress. 1-7 (2000)

[Publications] 小谷元子,砂田利一: "Zata fucehions on finite graphs"J.Marh.Sci.Univ.Tokyo. 7. 7-25 (2000)

[Publications] 小谷元子,砂田利一: "The pressune and higher correlations for an Auosov differworplisus"Erqod.Th.Dynam.Sys. (to appear).

[Publications] 小谷元子: "Higher correlations for an Anosiv flow"Aues.J.Math. (to appear).

[Publications] 芥川和雄: "Spin geometry, the Seiberg-Uithen eguiations and Yamabe invasiints of Kahler sufaces"Interdiscip.Inform.Sci.. 5. 55-72 (1999)

[Publications] 中西敏浩,M.Naatanen: "Areas of two-dinaousional moduli apaces"Proc.Aum.Math.Soc,. (to appear).

[Publications] 中西敏浩,M.Naataven G,Rosenberger: "Arithmetic Fuchsian groups of siguatuce (o;ei, er,es,en)with 2【less than or equal】e_1【less than or equal】e_2【less than or equal】e_3, en=∞"Couplex geometry of groups. (1999)

[Publications] 中西敏浩: "リーマン面上の割地線の長さとNielsenの実現問題"退化、被覆、特異点の代数幾向とトポロジー. 33-46 (2000)

[Publications] 小谷元子,砂田利一: "Jacobian fovi associated with a finite graple and its abelian couning graphs"Adu.Appl.Math.. 24. 89-110 (2000)

[Publications] 小谷元子,砂田利一: "Stund and veelizatron of crystal lattice via hainouic maps"Traw.Ames.Math.Soc.. 353. 1-20 (2001)

[Publications] 相山玲子,芥川和雄: "Kenmotsu type representation fornnla for spece like sunfaus in the de Sitha 3-space"Tsukuba J.Math.. 24. 189-196 (2000)

[Publications] 相山玲子,芥川和雄: "Kenmotsu type representation fovmula for surfaces with preseribed mean cuwatuse in the hypablic3-space"J.Math.Soc.Japan. 52. 877-898 (2000)

[Publications] 相山玲子,芥川和雄,Tom Y.M.Wan: "Hininal maps between the hyperbolic discs and genealped Qoues maps of maxineal simfaics in the auti-de siffer3-space"Tohoku Math.J.. 52. 415-429 (2000)

[Publications] 相山玲子,芥川和雄: "kenmotsu type representation forunla for surfaces with prescrived mean curoatue in the 3-sphere"Tohoku Math.J.. 52. 95-105 (2000)

[Publications] 相山玲子,芥川和雄: "Represeu tation formulas for surfaces in H^s(-C^2)and havmonic maps arising from CMC surfaces"Harmonic movphisms, Hamouic maps, and related topics. 275-285 (2000)

[Publications] 相山玲子,芥川和雄,宮岡礼子,梅原雅顕: "A global correspondence between CMC-Surfaces in S^3 and paices of non-conformal hamouic mapsinto S^2"Proc.Amer.Math.Soc.. 128. 939-941 (2000)

[Publications] 江尻典雄: "Homotopieally enesqy-minimizing hasimocne map of fori into RR^3"TokyoJ.Math. 23. 503-518 (2000)

[Publications] 金井雅彦: "力学系の不変幾何構造と剛性問題"数学. 52. 43-52 (2000)

[Publications] 金井雅彦: "A remanls on local rigidity of comfor〓l actions on the sphere"Math.Res.Lett. 6. 675-680 (1999)

[Publications] 小林亮一,逸見昌元: "Hoal's law in ptatistical manifolds and diver gances"Nayoya math.J.. 159. 1-24 (2000)

[Publications] 小林亮一: "Holomovphic curves in abelian vacieties : the second main theouew and appdicatious"Japan.J.Math.. 26. 129-152 (2000)

[Publications] 小林亮一,系川銚: "Msuimizing currents in open manifolds andf the n-1 homology of monue gatively Ricci curved niani folds"

内藤久資名古屋大学, 大学院・多元数理科学研究科, 助教授 (40211411)